Those "end of fight phase" things happen after consolidation, so you just get to select them *again* to fight after you've consolidated after the last fight. This includes pile-in and so on.
And I'm afraid I'm not quite following your Eversor example above, GML, vis-a-vis Heroic Intervention.
HI happens at the *start* of the fight phase (and no other time) so there's no way and Eversor could use it more than once. Then, sure, it could use a strat to let it fight again, but none of that has anything to do with whether anyone *in* the combat could target the Eversor with their attacks when it HI-ed into them.
If I have a unit that charges your unit, then your character slams into the combat, it seems obvious that my unit *should* be able to split its attacks among all eligible targets now engaged with it. That just seems silly and a clear oversight.
Now, the rules do say what they say, and I suppose the easiest way to handle this is just declare an assault on the random characters standing around, anyway (almost no reason not to), but it strikes me as not something so much designed as clearly unintentional.